1. Field of the Invention
The field of the invention is that of digital transmission, especially to mobiles. To be more precise, the invention concerns a method of constructing a spreading code associated with one user of a direct sequence code division multiple access (DS-CDMA) digital transmission system.
2. Description of the Prior Art
There are three major types of multiple access digital transmission systems, known as FDMA, TDMA and CDMA.
Historically, Frequency Division Multiple Access (FDMA) was the first of these systems to be used. It entails separating the calls to be transmitted by assigning each call a specific frequency band which can easily be separated from the others by filtering at the receiving end.
It is little used nowadays because it requires a receiver for each transmission channel used, so that a considerable number of receivers are required in a central station if it is to be possible to converse simultaneously with a large number of distributed stations.
The principle of Time Division Multiple Access (TDMA) is to time share the whole of the transmission channel. To prevent information overlapping, only one station sends at a time and, when it does send, it occupies all of the channel bandwidth.
TDMA systems encounter difficult problems with equalization if the transmission channel is disrupted by echoes or by jamming.
Finally, the Code Division Multiple Access (CDMA) system uses spread spectrum techniques.
One spectrum spreading technique is the direct sequence (DS-CDMA) technique which entails sending a signal s(t) obtained by multiplying a digital data signal d(t) by a spreading code g(t). The signal d(t) is characterized by its frequency, called the bit frequency. The spreading code g(t), which is specific to its user, is a pseudo-random signal characterized by its frequency, called the chip frequency. This frequency is greater than the bit frequency by a factor G known as the spreading gain or bandwidth expansion factor. The following equations apply:
data signal d(t): ##EQU1## spreading code g(t): ##EQU2## signal to be transmitted s(t): ##EQU3## where: T.sub.b is the reciprocal of the bit frequency;
T.sub.c is the reciprocal of the chip frequency; PA1 d.sub.k is the k(th) element of the summation for d(t); PA1 g.sub.k is the k(th) element of the summation for g(t); PA1 [ ] is the integer part. PA1 at least two different basic, in particular cyclically different, sub-codes belonging to the same family of basic sub-codes; and PA1 at least one secondary sub-code obtained by circular permutation of one of said basic sub-codes. PA1 the family of Gold codes; and PA1 the family of Kasami codes. PA1 .SIGMA. signifies concatenation; PA1 q is the concatenation index; PA1 n is the concatenation factor, i.e., the total number of sub-codes to be concatenated to form said spreading codes; PA1 T.sup.x is a circular permutation of x elements; PA1 a.sub.y is a basic sub-code of a family {ay} of basic sub-codes which can be used to construct the sub-codes to be concatenated; PA1 c.sub.k (q) is the function indicating the basic sub-code to be used to construct the q.sup.th sub-code to be concatenated in said k.sup.th spreading code; PA1 p.sub.k (q) is the function indicating the number of permutations to be effected on the basic sub-code a.sub.y to be considered, with y=c.sub.k (q). PA1 choosing a number K of available basic sub-codes; PA1 generating pairs (p.sub.k (q), c.sub.k (q)) iteratively from the spreading code index k in said family and then from the concatenation index q, said iterative generation entailing: PA1 V.sub.k (.sub.q)&lt;K.N where N is said period of the sub-codes; PA1 V.sub.k (q).noteq.V.sub.k (q') for all q'&lt;q, where q' corresponds to all values of q for which a pair (p.sub.k (q), c.sub.k (q)) has already been calculated; PA1 V.sub.k' (q).noteq.V.sub.k (q) for all k'&lt;k, where k' corresponds to all values of k for which a pair (p.sub.k (q), c.sub.k (q)) has already been calculated; PA1 the receive filtering is matched to the transmit filtering; PA1 an estimate of the impulse response of the channel exists; PA1 synchronization is acquired and perfect, so that the spreading code is perfectly reproduced at the receiving end and aligned with the transmitted spreading code. PA1 correlation of the received signal with the spreading code, enabling identification of the path signals which represent the contribution to the received signal of the various paths, and PA1 weighting of these path signals using the estimated impulse response of the channel, to produce an estimate of the data signal. PA1 to combat multi-user interference the spreading codes must have good partial aperiodic cross-correlation properties, and PA1 to combat intersymbol interference the spreading codes must have good partial aperiodic autocorrelation properties.
Decoding at the receiving end entails combining the received signal with a local replica of g(t) synchronized to the transmission.
In a DS-CDMA system there must be many spreading codes of the same family so that a large number of users can each have a different spreading code. The spreading codes must also be long enough to provide a specified minimal level of security against intentional jading, combined with confidentiality of transmission.
The invention applies mainly to the situation in which the receiving device is a diversity receiver, also known as a rake receiver.
It can be shown that with a rake receiver optimizing receive performance in the presence of multi-user interference requires the use of spreading codes having good partial aperiodic cross-correlation properties and that optimizing receive performance in the presence of intersymbol interference requires the use of spreading codes having good partial aperiodic autocorrelation properties.
In this context, "partial" means that the correlation is not effected over all of the period of the spreading code, and "aperiodic" means that the correlation is not effected merely by shifting two codes and correlating over a predetermined number of elements, but by correlating between elements corresponding to the same bits.
Partial aperiodic autocorrelation over a maximal number G of elements (where G is the spreading factor) of a code a.sub.i, for a starting index k.sub.1 and offset k.sub.2, can be defined using the following equation, for example: ##EQU4##
In the above equations, "mod" represents the mathematical function "modulo".
Likewise, partial aperiodic cross-correlation over a maximal number G of elements between two codes a.sub.i and a.sub.m for a starting index k.sub.1 and an offset k.sub.2 can be defined by the following equation, for example: ##EQU5##
The prior art spreading codes usually employed in conventional DS-CDMA systems have good correlation properties only if the correlations are effected over the entire period of the spreading codes. These prior art spreading codes, described for example in the document "Coherent Spread Spectrum Systems", J. K. Holmes, Wiley Interscience 1992 include the Gold and Kasami codes, for example.
Consequently, these prior art spreading codes cannot optimize the performance of a rake receiver since this requires spreading codes having good partial and aperiodic correlation properties.
In the specific case of an inversion type DS-CDMA system, i.e., when the spreading factor (or band expansion factor) is equal to the period of the spreading code, other types of code have been used in the prior art, namely structured codes.
Structured codes, described for example in the document "New signature code sequence design for CDMA systems", T. O'Farrell, Electronic Letters, 14 Feb. 1991, Vol. 27, are obtained by concatenating sub-codes (sometimes called short codes). The various sub-codes are obtained by circular permutation of a single starting sub-code. In other words, for a given structured code all of the sub-codes are the same except for their circular permutation.
These structured codes have particular correlation properties, especially aperiodic correlation properties. They have various drawbacks, however.
If L is the period of the original sub-code, there are L possible circular permutations. The period L' of the structured code is, therefore, at most equal to L.sup.2 (L'.ltoreq.L.sup.2). Structured codes, therefore, have the drawback of being relatively short and cannot achieve good confidentiality.
Also, the maximal number of structured codes in the same family, and therefore, the maximal number of users, is limited by K, the number of available cyclically different sub-codes. To construct a structured code associated with one user a single basic sub-code is concatenated several times with different phases.
An object of the invention is to palliate these various drawbacks of the prior art.
To be more precise, an object of the invention is to provide a method of constructing a family of spreading codes for a DS-CDMA system, with many spreading codes in the same family, of great length, and having good aperiodic partial autocorrelation and cross-correlation properties.
Thus an object of the invention is to provide spreading codes which optimize the performance of a rake receiver, especially in the presence of multi-user interference and intersymbol interference.